English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In an oligopolistic market, only a few firms account for most or all of total production, e.g., automobile, steel, and computer industries. For a dynamic oligopolistic market with two firms competing in quantities, we show that supervisory control theory of discrete event systems provides a novel approach to solve the dynamic oligopoly problem with the aim of maximizing the profits of both firms. Specifically, we show that the controllability, observability, and nonblocking property (which are the core concepts in supervisory control theory) are the necessary and sufficient conditions for two oligopolistic firms in disequilibrium to eventually reach equilibrium states of maximizing the profits of both firms. Keywords: discrete event systems, supervisory control, dynamic oligopoly, finite state automata I. INTRODUCTION In an oligopolistic market, only a few firms account for most or all of total production. Oligopoly is a prevalent form of market structure. Examples of oligopolistic industries include automobiles, steel, and computers. In this paper, we study an oligopolistic market with a homogenous good and competition in quantities. One representative model of such oligopolistic markets is the Cournot model consisting of two firms which must decide how much to produce to maximize their profits [4]. In a Cournot equilibrium, each firm is producing an amount that maximizes its profit given what its competitor is producing, so neither would want to change its output. Thus the Cournot equilibrium is an example of Nash equilibrium. When two firms are initially producing output levels that differ from the Cournot equilibrium, is it always possible for the firms to reach the equilibrium eventually?; how do they adjust their outputs until the equilibrium is reached? These dynamic oligopoly problems have been studied by many economists [1,6,11] based on the assumption that each firm exactly knows the last strategies of its rival firms and also market demand. In this paper, we study the dynamic oligopoly problem using supervisory control theory of discrete event systems (DESs) [10] modelled by finite state automata. In [8], it has been shown that a competitive market can be modelled as a finite state automaton. A dynamic oligopolistic market also has event-driven dynamics, e.g., the state (outputs of firms and a price) of the market changes according to an event (action or decision) of a firm such as increasing output or decreasing it. In general, such an event occurs irregularly. In this paper, we construct a finite state automaton describing the dynamic behavior of each oligopolistic firm. The model describes how a state (comprised of output and marginal cost) of a firm changes by the events of increasing output, decreasing output, and uncontrollable fluctuations of production cost by exogenous causes. Moreover we model the behavior of a market demand to describe how a state (comprised of total output and price) of the market demand changes by the events of increasing outputs and decreasing outputs of firms, and uncontrollable demand fluctuations by exogenous causes. From these component models, we construct a composite model of the market which describes overall behaviors of firms and market demand. Based on the model, this paper presents the controllability, observability, and nonblocking property to assure that an oligopolistic market in disequilibrium can always reach an equilibrium in the presence of uncontrollable fluctuations of production cost and market demand caused by exogenous factors. The major differences between our approach and conventional approaches by economists are as follows. (1) Conventional differential or difference equation models do not effectively capture uncontrollable changes in production cost and market demand caused by exogenous factors. They usually deal with fixed situations in which marginal costs and market demands are given as fixed (may be constants or linear curves). However, discrete event models presented in this paper are suitable for modeling such uncontrollable changes of an oligopolistic market. (2) Conventional works usually assume that each firm exactly knows the last strategies of its rival firms and a market demand. However, this paper assumes that each firm does not exactly know its rivals' outputs and marginal costs. Many economists estimate a rival's past output through current information such as price. However,

Supervisory Control of Dynamic Oligopolistic Markets: How can Firms Reach Profit-Maximization?